Translator Disclaimer
15 August 2020 A proof of the multiplicity 1 conjecture for min-max minimal surfaces in arbitrary codimension
Alessandro Pigati, Tristan Rivière
Duke Math. J. 169(11): 2005-2044 (15 August 2020). DOI: 10.1215/00127094-2020-0002

Abstract

Given any admissible k -dimensional family of immersions of a given closed oriented surface into an arbitrary closed Riemannian manifold, we prove that the corresponding min-max width for the area is achieved by a smooth (possibly branched) immersed minimal surface with multiplicity 1 and Morse index bounded by k .

Citation

Download Citation

Alessandro Pigati. Tristan Rivière. "A proof of the multiplicity 1 conjecture for min-max minimal surfaces in arbitrary codimension." Duke Math. J. 169 (11) 2005 - 2044, 15 August 2020. https://doi.org/10.1215/00127094-2020-0002

Information

Received: 31 August 2018; Revised: 6 December 2019; Published: 15 August 2020
First available in Project Euclid: 8 July 2020

MathSciNet: MR4132579
Digital Object Identifier: 10.1215/00127094-2020-0002

Subjects:
Primary: 49Q05
Secondary: 49Q15, 49Q20, 58E20

Rights: Copyright © 2020 Duke University Press

JOURNAL ARTICLE
40 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.169 • No. 11 • 15 August 2020
Back to Top